Simplify Square Root of 39401

Here we will show you two methods that you can use to simplify the square root of 39401. In other words, we will show you how to find the square root of 39401 in its simplest radical form using two different methods.

To be more specific, we have created an illustration below showing what we want to calculate. Our goal is to make "A" outside the radical (√) as large as possible, and "B" inside the radical (√) as small as possible.

√39401 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 39401 to simplify the square root of 39401. This is how to calculate A and B using this method:

A = Calculate the square root of the greatest perfect square from the list of all factors of 39401. The factors of 39401 are 1, 31, 41, 961, 1271, and 39401. Furthermore, the greatest perfect square on this list is 961 and the square root of 961 is 31. Therefore, A equals 31.

B = Calculate 39401 divided by the greatest perfect square from the list of all factors of 39401. We determined above that the greatest perfect square from the list of all factors of 39401 is 961. Furthermore, 39401 divided by 961 is 41, therefore B equals 41.

Now we have A and B and can get our answer to 39401 in its simplest radical form as follows:

√39401 = A√B

√39401 = 31√41

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 39401 to simplify the square root of 39401 to its simplest form possible. This is how to calculate A and B using this method:

A = Multiply all the double prime factors (pairs) of 39401 and then take the square root of that product. The prime factors that multiply together to make 39401 are 31 x 31 x 41. When we strip out the pairs only, we get 31 x 31 = 961 and the square root of 961 is 31. Therefore, A equals 31.

B = Divide 39401 by the number (A) squared. 31 squared is 961 and 39401 divided by 961 is 41. Therefore, B equals 41.

Once again we have A and B and can get our answer to 39401 in its simplest radical form as follows:

√39401 = A√B

√39401 = 31√41

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Simplify Square Root of 39402
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